Private Value Auctions Research Articles

Financial Bubbles in Infinitely Repeated Auctions with Tokens

An auctioneer holds an infinite sequence of private value auctions. He can accept payments in a blockchain-based token that he creates and initially owns. I show that relative to a standard auction with dollars, the present-discounted value of the expected revenues is higher whenever financial bubbles on tokens emerge, which happens when the rate at which investors use their tokens for bidding is sufficiently low. Financial bubbles can also emerge if the auctioneer uses dollars and issues equity. But in this case, a bubble is possible only if an increasing amount of aggregate wealth is invested in equity, which seems counterfactual.

The Winner’s Curse in Dynamic Forecasting of Auction Data: Empirical Evidence from eBay

Problem definition: Dynamic forecasting models in auctions have fallen short on two dimensions: (i) the lack of an equilibrium model for final bids and (ii) the lack of a winner’s curse (i.e., a tendency to overpay conditional on winning the auction) adjustment to allow bidders to account for a common value component in the auction item. In this paper, we develop a methodology to accurately predict equilibrium stage bids from the initial bidding dynamics and quantify the impact of the winner’s curse. This methodology allows us to conduct policy simulations to optimize auction design parameters. Methodology/Results: Dynamic auctions typically have a stage of high exploratory activity, followed by an inactivity period, and then an equilibrium stage of last-minute bids with sharp jumps. With a Kalman filter approach, we use exploratory stage bids to predict an auction item’s valuation distribution. We feed this prediction into an equilibrium model and apply item-specific adjustments for winner’s curse, bidder heterogeneity, and inactivity period. We use the resulting equilibrium model to predict the equilibrium stage bids. Our methodology improves the forecast of equilibrium stage bids by 11.33%, on average, compared with a state-of-the-art benchmark. This improvement is even higher (18.99%) for common value auctions. We also find that (i) significantly more (respectively, fewer) bidders internalize the winner’s curse in common value (respectively, private value) auctions; (ii) bidders in common value auctions decrease their bids by 6.03% because of the winner’s curse; and (iii) the inactivity period has a lesser impact on the equilibrium stage bids in private value auctions. Managerial implications: Our proposed methodology is intended to facilitate the need in academia and practice for real-time bid predictions that encompass different levels of the common value component in auctions. Using our methodology, auction platforms can support their choice of minimum bid increment policies and decide how to allocate resources across different auctions to mitigate the adverse effects of the winner’s curse. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2022.1165 .

Distributionally robust pricing in independent private value auctions

A seller chooses a reserve price in a second-price auction to maximize worst-case expected revenue when she knows only the mean of value distribution and an upper bound on either values themselves or variance. Values are private and iid. Using an indirect technique, we prove that it is always optimal to set the reserve price to the seller's own valuation. However, the maxmin reserve price may not be unique. Sometimes it is optimal to choose a deterministic reserve price even when randomization is allowed, which is unusual for maxmin settings. A second-price auction with the reserve equal to seller's value is an asymptotically optimal mechanism (among all ex post individually rational mechanisms) as the number of bidders grows without bound.

Level-k Models and Overspending in Contests

The experimental evidence on contests often reports overspending of contest participants compared to the theoretical Nash equilibrium outcome. We show that a standard level-k model may rationalize overspending in contests. This result complements the existing literature on overspending in contests, and it bridges an open gap between the contest and auction literature. In fact, the literature on auctions often runs parallel to that on contests.Overbidding in auctions has also been documented empirically, and it has been shown that, in private-value auctions, such overbidding can be rationalized by level-k reasoning. We bridge the existing gap between the auction and contest literature by showing that overbidding may also be true in a theoretical contest environment with level-k reasoning.

Auctions with flexible information acquisition

We consider independent private value auctions in which prior to bidding, each bidder engages in fully flexible information acquisition, choosing not only how much information but also what information to acquire about his value. Focusing on a tractable environment with binary underlying values and posterior-separable information costs, we characterize the unique symmetric equilibrium and investigate the effects of information costs on auction outcomes. We also analyze how the reserve price influences bidders' information-acquisition behavior and study its implications for the seller's expected revenue.

Uninformed Bidding in Sequential Auctions

Abstract We consider a private-value auction with one-sided incomplete information in which two objects are sold in a sequence of two second-price auctions. The buyers have multiunit demand and are asymmetrically informed at the ex ante stage of the game. One buyer perfectly knows his type, and the other buyer is uninformed about her own type. We consider interim information acquisition by the uninformed buyer and derive an asymmetric equilibrium that is shown to produce a declining price sequence across both sales. The supermartingale property of the price sequence stems from the uninformed buyer’s incentives to gather private information, which leads to aggressive bidding in the first-stage auction.

Availability of Substitutes, Information Effects, and Bidding Behavior in Private Value Auction Experiments

Availability of Substitutes, Information Effects, and Bidding Behavior in Private Value Auction Experiments

Reference Price Effects in First-price Private-value Auctions

External reference points, such as outside options or budget constraints, are common in bidding environments. We experimentally investigate the impact of external reference points for bidding in first-price auctions with independent private values. We find that the presence of a reference point distorts bidding behaviour. There are “reference price effects” consistent with a preference for certainty and anchoring bias. To establish robustness, we conduct a second experiment that controls for bidders’ first-order beliefs. After controlling for beliefs, the reference price effect dominates. We observe that the imposition of a ceiling on the opponent’s maximum bid set at the upper bound of the risk-neutral Nash equilibrium support is strong enough to reverse the well-documented pattern of overbidding in first-price auctions and indeed to induce significant underbidding. The findings inform on the implications of auction formats that involve reference points, and specifically buy-it-now price options that are common in internet auction listings.

Rational inattention and the monotone likelihood ratio property

This paper explores the connection between rational inattention and the monotone likelihood ratio property (MLRP). In many economic problems, agents prefer to take a higher action when there is a higher underlying state. It is often assumed that these agents have noisy signals that are strongly correlated with the underlying state, i.e. ordered by the MLRP. Separately, a large literature has recently explored the behavior of rationally inattentive agents. Under some common separability and smoothness assumptions on the class of attention costs, I show that agents will always acquire signals that are ordered by the MLRP within such economic problems if and only if they have attention costs proportional to entropy reduction. With any other attention costs, agents err regarding the relative benefit of actions at different states. Extending to games, I provide conditions under which players first acquire MLRP-ordered signals, and then choose higher actions given higher signals. I then apply these results to independent private-value auctions.

Auction theory and its practical application

Introduction.The large-scale use of auctions today in various fields, while avoiding distortions in the behavior of economic agents is considered by scientists as one of the effective tools to improve public welfare. Research conducted by Nobel Laureates in Economics 2020 Paul Milgrom and Robert Wilson has made it possible to rethink the possibilities of reformatting auctions to ensure the maximum benefit from their holding for all subjects. P. Milgrom and R. Wilson demonstrated how the technically complex«constructions» of economics to build optimal auction designs make it possible to obtain complete material benefits for society.Prupose.To substantiate the specifics of auction theory, the formats of the latter and the contribution to their development of P. Milgrom and R. Wilson - winners of the Nobel Prize in Economics in 2020.Methods. During the preparation of the article general scientific research methods were used: analysis, synthesis, induction, deduction, as well as the method of formalization, which greatly contributed to the possibility of identifying the specifics of auction theory, their formats and substantiation of scientific achievements of Nobel Laureates in Economics P. Milgrom and R. Wilson in the development of theory and practice of auctions.Results. Research by P. Milgrom and R. Wilson, awarded the Nobel Prize «for improvements to auction theory and inventions of new auction formats»), prove that auction theory is an effective tool for regulators and governments of different countries that are interested in finding ways to most effectively use certain assets. Unlike most economic models, which usually require simplification and abstraction, the conclusions of scientists in auction theory can be applied in a specific practical area - from trade in raw materials and securities - to public procurement, tenders, subsoil and radio frequency, online advertising, etc. While previous researchers, including W. Vickrey and R. Myerson, devoted their work to private value auctions (when for each buyer the value of the object is known only to him and does not depend on the opinion of other auction participants), R. Wilson in the late 1960s, focused on the analysis of auctions with common value (when the object is of equal value to all auction participants, but each of them may have its own unique information about it). In particular, at auctions for the right to produce oil in a certain area, its value for all bidders is the same, but information on the field reserves and the specifics of the area may be different. R. Wilson also argued what should be the behavior of a rational bidder to avoid the so-called «winner’s curse» (a situation in which the winner of the object will pre- set an excessively high price, if guided solely by their own assessment of profits). Radio frequency auctions in the United States are the largest and best-known example of the practical application of the findings of R. Wilson and P. Milgrom, which made the previously inefficient and virtually free distribution of licenses a way to win for sellers and buyers and society as a whole.Discussion. Auction theory will continue to develop in the future, taking into account the new challenges posed, in particular, the need to develop tools and mechanisms for conducting virtual auctions in order to adequately adapt to digital reality. The need to develop a «road map» to address the shortcomings inherent in the existing auction formats in terms of taking into account the accelerated development of technology, increasing mobility, globalization and digitalization of the economy.

Uninformed Bidding in Sequential Auctions

We consider a private value auction with one-sided incomplete information in which two objects are sold in a sequence of two second-price auctions. Buyers have multi-unit demands and both are asymmetrically informed at the ex-ante stage of the game. One buyer perfectly knows his type and the other is uninformed about his own type. We con-sider interim information acquisition for the uninformed buyer and derive an asymmetric equilibrium which is shown to produce a declining price sequence across both sales. The supermartingale property of the price sequence stems from the uninformed buyer’s incen-tives to gather private information which leads to an aggressive bidding at the first-stage auction.

Auctions with signaling concerns

AbstractWe study a symmetric private value auction with signaling, in which the auction outcome is used by an outside observer to infer the bidders' types. We elicit conditions under which an essentially unique D1 equilibrium bidding function exists in the second‐price and the English auctions. We establish there is no equivalence between these two auction designs, neither in bidding strategies nor in expected revenue. This is because the presence or the absence of an increasing price clock affects signaling incentives differently in both auction formats, and thereby also the bidders' incentives to overbid their types. This leads to a strictly higher expected revenue in the second‐price auction than in the English auction. Our analysis is completed by a comparison with other disclosure policies. Applications include art auctions and charity auctions.

AUCTIONS WITH LEAKS ABOUT EARLY BIDS: ANALYSIS AND EXPERIMENTAL BEHAVIOR

In sequential first‐ and second‐price private value auctions, second movers are informed about the first movers' bid with commonly known probability. Equilibrium bidding in first‐price auctions is mostly unaffected, but there are multiple equilibria in second‐price auctions affecting comparative statics across price rules. We show experimentally that informational leaks in first‐price auctions qualitatively confirm the theoretical predictions. In second‐price auctions, we analyze and experimentally confirm the existence of focal equilibria, and provide evidence for individual consistency in equilibrium selection. (JEL D44, C72, C91)

A Bayesian Level-k Model in n-Person Games

In standard models of iterative thinking, players choose a fixed rule level from a fixed rule hierarchy. Nonequilibrium behavior emerges when players do not perform enough thinking steps. Existing approaches, however, are inherently static. This paper introduces a Bayesian level-k model, in which level-0 players adjust their actions in response to historical game play, whereas higher-level thinkers update their beliefs on opponents’ rule levels and best respond with different rule levels over time. As a consequence, players choose a dynamic rule level (i.e., sophisticated learning) from a varying rule hierarchy (i.e., adaptive learning). We apply our model to existing experimental data on three distinct games: the p-beauty contest, Cournot oligopoly, and private-value auction. We find that both types of learning are significant in p-beauty contest games, but only adaptive learning is significant in the Cournot oligopoly, and only sophisticated learning is significant in the private-value auction. We conclude that it is useful to have a unified framework that incorporates both types of learning to explain dynamic choice behavior across different settings. This paper was accepted by Manel Baucells, decision analysis.

Instrumental variables estimation of a simple dynamic model of bidding behavior in private value auctions

We provide the first, in experimental economics, consistent estimates of a dynamic learning model with a continuous outcome. The econometric approach we propose can be used in many experimental studies including auctions, bargaining with transfers, and gift exchange experiments. We focus on affiliated private value auctions, where subjects are generally assumed to converge to the rule-of-thumb bidding, but our general approach is applicable to many other settings. Our IV estimates suggest that subjects become significantly less aggressive over time; specifically, they decrease their bids in proportion to the previous period’s signal minus bid. However, the inconsistent OLS and FE estimators imply that subjects become significantly more aggressive over time—they raise their bids in proportion to the previous period’s signal minus bid. Our instruments are randomly generated by the experiment, and pass popular weak instrument tests.

Reference-Dependent Preferences and Overbidding in Private and Common Value Auctions

This paper proposes a model of reference dependent preferences to explain overbidding in private and common value auctions. It is assumed that the reference point is proportional to the value of the object and that losses are weighed more heavily than gains in the utility function. Equilibrium bidding strategies are derived for first- and second-price private and common value auctions. I find that this model fits the data of all experiments analyzed, both private and common value, better in terms of the Bayesian Information Criterion than a standard risk neutral model; moreover, it explains overbidding in all private value and some common value auctions better than other alternative models. These results suggest that reference dependence, among other factors, might play a role in the widespread tendency of subjects to overbid in most experimental auctions.

The Winner's Curse in Dynamic Forecasting of Auction Data: Empirical Evidence from eBay

Problem definition: Dynamic forecasting models in auctions have fallen short on two dimensions: (i) the lack of an equilibrium model for final stage bids and (ii) the lack of a winner's curse (i.e., a tendency to overpay conditional on winning the auction) adjustment to allow bidders to account for a common value component in the auction item. In this paper, we develop a methodology to accurately predict final stage bids from the initial bidding dynamics and quantify the impact of the winner's curse. This methodology allows us to conduct policy simulations to optimize auction design parameters. Methodology: Dynamic auctions typically have a stage of high exploratory activity, followed by an inactivity period, and then a final stage of last-minute bids with sharp jumps. With a Kalman filter approach, we use exploratory stage bids to predict an auction item's valuation distribution. We feed this prediction into an equilibrium model and apply item-specific adjustments for winner's curse, bidder heterogeneity, and inactivity period. We use the resulting equilibrium model to predict the final stage bids. Results: Our methodology improves the forecast of final stage bids by 15.84%, on average, compared to a state-of-the-art benchmark. This improvement is even higher (22.44%) for common value auctions. We also find that: (i) significantly more (resp., fewer) bidders internalize the winner's curse in common value (resp., private value) auctions, (ii) bidders in common value (resp., private value) auctions decrease their bids by 6.69% (resp., 3.51%) due to the winner's curse, and (iii) the inactivity period has a lesser impact on the final stage bids in private value auctions. Managerial Implications: Our proposed methodology is intended to facilitate the need in academia and practice for real-time bid predictions that encompass different levels of the common value component in auctions. Using our methodology, auction platforms can support their choice of minimum bid increment policies and decide how to allocate resources across different auctions to mitigate the adverse effects of the winner's curse.

Urban Environmental Evaluation Using Affiliated Private Value Auction Model

This study evaluates the policy that brings non-marginal changes in an urban environmental attribute, fire risk, by using real estate auction data. Our evaluation is based on the extrapolation of the value distribution for auctioned real estate. In the estimation, we propose a simulated method of moments that is based on the moment conditions on order statistics of bids. We consider the possibility of affiliation by applying the Archimedean copula. Our estimation result rejects the hypothesis that bidders' valuation for apartments is independent when we assume that the marginal distribution of value follows log-normal or exponential distributions.

Auctions with Signaling Concerns

We study a symmetric private value auction with signaling, in which the auction outcome is used by an outside observer to infer the bidders' types. We elicit conditions under which an essentially unique D1 equilibrium bidding function exists in four auction formats: first-price, second-price, all-pay and the English auction. We obtain a strict ranking in terms of expected revenues: the first-price and all-pay auctions dominate the English auction but are dominated by the second-price auction.

Analysis of the Sarbanes-Oxley Ban on Non-Audit Services From an Auction Model Perspective

This study analyzes the impact of the Sarbanes-Oxley Act’s (SOX) ban on providing both auditing and nonaudit services by auditors to their clients. We use a first-price private value auction to compare a setting in which auditors can compete for both audit and nonaudit services with an auction in which they can compete for only one of the two services. Consistent with empirical studies, we show that the ban on nonaudit services results in fee hikes for both audit and nonaudit services, as the number of bidders (audit firms) is smaller in the post-SOX setting relative to pre-SOX setting in both auctions. Consequently, we demonstrate that, after the ban, payoffs have increased for audit firms and decreased for their clients, due to the increase in both audit and nonaudit services fees. Finally, we show that increasing the penalty for an audit failure, contrary to common wisdom, results in improved payoffs for audit firms.